Allardyce, 61, recently took the reins at Sunderland, and is charged with the task of reversing the Black Cats' fortunes after a dismal few years at the Stadium of Light.
His latest job comes just five months after leaving West Ham, where his departure was confirmed on the final day of last season after a 2-0 defeat away to Newcastle United.
It may be some time since he left Upton Park, but Allardyce has reflected on one particular transfer deal during his time with the club in his new book 'Big Sam'.
The Sunderland Echo quote that Allardyce tells a story about his interest in signing Connor Wickham for West Ham, but couldn't force a deal through for a player he compared to Kevin Davies.
"I don’t mind admitting I wanted Connor Wickham from Sunderland," said Allardyce. "He was underperforming for them, but I felt we would play to his strengths and he would get us goals and assists the way Kevin Davies did for Bolton."
"Sunderland wouldn’t play ball though, despite us being encouraged to go for it by his agent who was sure they would let him leave for £8million. It turned out that wasn’t the case," he added.
Wickham was ironically sold by Sunderland over the summer, as the forward is now playing for Crystal Palace - and you have to assume that there is no way Allardyce would have sanctioned that deal had he been in charge.
As for West Ham, they now have Diafra Sakho, Enner Valencia, Andy Carroll and Nikica Jelavic as their attacking options, and Wickham - who has often struggled to score goals in the Premier League - wouldn't really have much of a role amongst those players.